Question

Payday loans are very short-term loans that charge very high interest rates. You can borrow $200 today and repay $250 in two weeks. What is the compound annual rate implied by this 25 percent rate charged for only two weeks?

32,987.22 percent

30.00 percent

128.25 percent

26.60 percent

Answer 1

32,987.22 percent

Step-by-step explanation:

The rate charged for 2 weeks is 25%, which means that after every 2 weeks the interest rate is compounded. Now in order to find the annual compounded rate we will use the formula (1+Weekly return)^Number of compounding periods)-1)

In this case there are around 52 weeks in a year and because interest is compounded every 2 weeks, there will be 26 compounding periods in a year.

So we put these numbers in our formula

((1+0.25)^26-1)=330.8722-1=329.8722

Now in order to find the percentage we will multiply 329.8722 by 100

=32,987.22%

This is our compounded annual rate.